Two identical circles intersect so that their centers, and the points at which they intersect, form a square of side 1 cm. The area in sq. cm of the portion that is common to the two circles is:
Given, perimeter of a equilateral triangle and regular hexagon are equal
6r=3a
=> a/r = 2
So Ratio of their areas = (sqrt(3)/4)a^2 : 3sqrt(3)/2 r^2
=> a^2/r^2 : 3*2
=> 4:6 => 2:3
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Find the ratio of the area of square to area of triangle.
Diagonal of a square = 2a
Area of the square = 1/2*(diagonal)^2 = 2a^2
Side of the equi triangle is a
Area of equilateral triangle = (_/3/4)a^2
so Ratio of Area of Triangle to Square = (_/3/4)a^2 : 2a^2 = _/3:8
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A circular swimming pool is surrounded by a concrete wall 4ft wide. If the area of the wall is 11/25 of the area of the pool then radius of the pool in feet is
A square field of side 500 m each is surrounded by a compound wall. A fence is to made such that it encloses a triangle formed by two compound walls and the fence. If the length of the fence is 100m then the maximum possible area in square metres of the triangle can be :
The triangle has to be max area and hence should be equilateral but cannot be as the angle in the sq shall be 90 degrees. Hence the triangle is isosceles with the angles as 90, 45, 45. Hence the other two sides shall be 50Ö 2 each. So area is 0.5 x base x ht etc. etc.
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The figure below shows 2 concentric circles with centre O. PQRS is a square inscribed in the outer circle. It also circumscribes the inner circle touching it at points B, C, D and A. What is the ratio of the Perimeter of the outer circle to that of the polygon ABCD.
If R is the radius of outer circle, then the side of the innermost square = R. Required answer = 2p r/4r = p /2.
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A circle circumscribes three unit circles that touch each other. What is the area of the larger circle? Note that p is the ratio of the circumference to the diameter of a circle (3.14159265).
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